Q.58 - The Practice of Statistics for AP

Question

Which of the following explains why one of the conditions for performing the chi-square test is met in this case? 

(a) The sample is large, $4877$ teenagers in all. 

(b) The sample is random. 

(c) All the observed counts are greater than $100$.

(d) We used software to do the calculations. 

(e) Both variables are categorical. 

Step-by-Step Solution

Answer

The options (b),(c) and (e) are satisfied here.

Step 1: Given Information

The conditions for performing the chi-square test are met in this case.

Step 2: Explanation

The Chi-square test is determined based on the following conditions are being met:

1) The sampling method used mainly is simple random sampling.

2) The variable under study is categorical

3) The expected value of the number of samples in each level of the variable is at least $5$.

Here, the sample is random, all observed counts are greater than $100$ and both variables are categorical.

So, all the conditions are met and the chi-square test can be performed.

Therefore, options (b), (c), and (e) are satisfied here.